The long-term goal of the proposed project is to develop flexible semi parametric analysis tools for cancer research in both epidemiologic studies and clinical trials. The change in title from the previous award reflects the completion of most of the aims in the original grant (R29 CA75 142) as well as a greater emphasis on semi parametric and empirical process methods which played an increasingly important role throughout the previous grant's multivariate clinical trial research. Semi parametric models are useful in medical research because they involve both a parametric component which is usually easy to interpret and a nonparametric component which permits greater flexibility in the presence of biologic uncertainty. The three proposed interrelated aims are: (1) Develop and evaluate inferential methods for semi parametric proportional hazards frailty regression models to account for unobserved individual-level heterogeneity in time-to-event data; (2) Develop and evaluate tools for flexible semi parametric risk-factor testing in cancer studies; and (3) Create tools for computationally efficient inference for survival, quantile and hazard functions in semi parametric models. The primary statistical research methods used for these challenging and interrelated aims include empirical process and semi parametric inference techniques as well as Monte Carlo computational approaches. These aims will provide cancer researchers with a significantly improved collection of useful modeling tools.